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Simplifying 4t2 + 5t + -20 = 0 Reorder the terms: -20 + 5t + 4t2 = 0 Solving -20 + 5t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + 1.25t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 1.25t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + 1.25t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1.25t + t2 = 0 + 5 1.25t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 1.25t + t2 = 5 The t term is 1.25t. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25t + 0.390625 + t2 = 5 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = 5 + 0.390625 Combine like terms: 5 + 0.390625 = 5.390625 0.390625 + 1.25t + t2 = 5.390625 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = 5.390625 Calculate the square root of the right side: 2.321771953 Break this problem into two subproblems by setting (t + 0.625) equal to 2.321771953 and -2.321771953.Subproblem 1
t + 0.625 = 2.321771953 Simplifying t + 0.625 = 2.321771953 Reorder the terms: 0.625 + t = 2.321771953 Solving 0.625 + t = 2.321771953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = 2.321771953 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = 2.321771953 + -0.625 t = 2.321771953 + -0.625 Combine like terms: 2.321771953 + -0.625 = 1.696771953 t = 1.696771953 Simplifying t = 1.696771953Subproblem 2
t + 0.625 = -2.321771953 Simplifying t + 0.625 = -2.321771953 Reorder the terms: 0.625 + t = -2.321771953 Solving 0.625 + t = -2.321771953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = -2.321771953 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = -2.321771953 + -0.625 t = -2.321771953 + -0.625 Combine like terms: -2.321771953 + -0.625 = -2.946771953 t = -2.946771953 Simplifying t = -2.946771953Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.696771953, -2.946771953}
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